Three Regions Tariff Model
D. Riker, 05/13/19 version
This partial equilibrium (PE) model of ad valorem tariffs has three sources of supply and three regional markets, labeled A, B, and C. Consumer demands have a non-nested CES form for the products of the industry. Total industry demand in the region has a constant price elasticity that is region-specific. The supply for each of the three sources has a constant price elasticity. The data inputs of the model are the initial expenditures, initial tariffs, and revised tariffs. The parameter inputs of the model are the elasticity of substitution, the price elasticity of total demand, and the price elasticity of each of the sources of supply. The model also includes demand and supply shift parameters that are calibrated to initial market equilibrium prices and quantities.

The model simulates the effects on prices, quantities, and consumer expenditures of a change in ad valorem tariff rates.

The user can modify data inputs, elasticity values, and tariff rates in the simulation by change the values in the ORANGE-shaded lines in the notebook below tab. The spreadsheet will  update the estimated changes in economic outcomes that are reported in the GREEN-shaded cells once the user selects "Evaluate Notebook" under "Evaluation" in the Menu above.

This model is provided as a generic analytical tool, and the data and parameter values are fictional and illustrative. Actual data and parameter values should be supplied by the user based on the industry and market to which the model is applied. The model is the result of ongoing professional research of USITC staff and may be updated. The model is not meant to represent in any way the view of the U.S. International Trade Commission or any of its individual Commissioners. The model is posted to promote the active exchange of ideas between USITC staff and experts outside the USITC and to provide useful economic modeling tools to the public.

In[1]:= ClearAll[f];
Parameter Inputs
Elasticity of Substitution
In[2]:= sigma=3;
Total Industry Price Elasticity of Demand
In[3]:= etaA=-1;
In[4]:= etaB=-1;
In[5]:= etaC=-1;
Supply Elasticity Parameters
In[6]:= eA=5;
In[7]:= eB=5;
In[8]:= eC=5;
Initial Ad Valorem Tariffs
In[9]:= tBA0=0.10;
In[10]:= tCA0=0.00;
In[11]:= tAB0=0.00;
In[12]:= tAC0=0.00;
In[13]:= tBC0=0.00;
In[14]:= tCB0=0.00;
Revised Ad Valorem Tariff
In[15]:= tBA=0.00;
In[16]:= tCA=0.00;
In[17]:= tAB=0.00;
In[18]:= tAC=0.00;
In[19]:= tBC=0.00;
In[20]:= tCB=0.00;
Initial Equilibrium Values
Expenditures in A
In[21]:= vAA0=100;
In[22]:= vBA0=100;
In[23]:= vCA0=100;
Expenditures in B
In[24]:= vBB0=100;
In[25]:= vAB0=100;
In[26]:= vCB0=100;
Expenditures in C
In[27]:= vCC0=100;
In[28]:= vBC0=100;
In[29]:= vAC0=100;
Prices
In[30]:= pA0=1;
In[31]:= pB0=1;
In[32]:= pC0=1;
Quantities from A
In[33]:= qAA0=vAA0/pA0;
In[34]:= qBA0=vBA0/(pB0 (1+tBA0));
In[35]:= qCA0=vCA0/(pC0 (1+tCA0));
Quantities from B
In[36]:= qBB0=vBB0/pB0;
In[37]:= qAB0=vAB0/(pA0 (1+tAB0));
In[38]:= qCB0=vCB0/(pC0 (1+tCB0));
Quantities from C
In[39]:= qCC0=vCC0/pC0;
In[40]:= qBC0=vBC0/(pB0 (1+tBC0));
In[41]:= qAC0=vAC0/(pA0 (1+tAC0));
Calibration of Parameters Based on the Initial Equilibrium
In[42]:= aA=(vAA0/pA0+vAB0/(pA0 (1+tAB0))+vAC0/(pA0 (1+tAC0))) pA0^-eA;
In[43]:= aB=(vBB0/pB0+vBA0/(pB0 (1+tBA0))+vBC0/(pB0 (1+tBC0))) pB0^-eB;
In[44]:= aC=(vCC0/pC0+vCA0/(pC0 (1+tCA0))+vCB0/(pC0 (1+tCB0))) pC0^-eC;
In[45]:= bAB=(vAB0 ((pA0 (1+tAB0))/pB0)^(sigma-1))/vBB0;
In[46]:= bAC=(vAC0 ((pA0 (1+tAC0))/pC0)^(sigma-1))/vCC0;
In[47]:= bBA=(vBA0 ((pB0 (1+tBA0))/pA0)^(sigma-1))/vAA0;
In[48]:= bBC=(vBC0 ((pB0 (1+tBC0))/pC0)^(sigma-1))/vCC0;
In[49]:= bCA=(vCA0 ((pC0 (1+tCA0))/pA0)^(sigma-1))/vAA0;
In[50]:= bCB=(vCB0 ((pC0 (1+tCB0))/pB0)^(sigma-1))/vBB0;
In[51]:= PA0=(pA0^(1-sigma)+bBA (pB0 (1+tBA0))^(1-sigma)+bCA (pC0 (1+tCA0))^(1-sigma))^(1/(1-sigma));
In[52]:= PB0=(pB0^(1-sigma)+bAB (pA0 (1+tAB0))^(1-sigma)+bCB (pC0 (1+tCB0))^(1-sigma))^(1/(1-sigma));
In[53]:= PC0=(pC0^(1-sigma)+bBC (pB0 (1+tBC0))^(1-sigma)+bAC (pA0 (1+tAC0))^(1-sigma))^(1/(1-sigma));
In[54]:= kA=vAA0 PA0^(-sigma-etaA) pA0^(sigma-1);
In[55]:= kB=vBB0 PB0^(-sigma-etaB) pB0^(sigma-1);
In[56]:= kC=vCC0 PC0^(-sigma-etaC) pC0^(sigma-1);
New Equilibrium Values with Revised Tariff
In[57]:= PA=(pA^(1-sigma)+bBA (pB (1+tBA))^(1-sigma)+bCA (pC (1+tCA))^(1-sigma))^(1/(1-sigma));
In[58]:= PB=(pB^(1-sigma)+bAB (pA (1+tAB))^(1-sigma)+bCB (pC (1+tCB))^(1-sigma))^(1/(1-sigma));
In[59]:= PC=(pC^(1-sigma)+bBC (pB (1+tBC))^(1-sigma)+bAC (pA (1+tAC))^(1-sigma))^(1/(1-sigma));
In[60]:= EqnA1=aA pA^eA==kA PA^(sigma+etaA) pA^-sigma+kB PB^(sigma+etaB) (pA (1+tAB))^-sigma bAB+kC PC^(sigma+etaC) (pA (1+tAC))^-sigma bAC;
In[61]:= EqnB1=aB pB^eB==kB PB^(sigma+etaB) pB^-sigma+kA PA^(sigma+etaA) (pB (1+tBA))^-sigma bBA+kC PC^(sigma+etaC) (pB (1+tBC))^-sigma bBC;
In[62]:= EqnC1=aC pC^eC==kC PC^(sigma+etaC) pC^-sigma+kA PA^(sigma+etaA) (pC (1+tCA))^-sigma bCA+kB PB^(sigma+etaB) (pC (1+tCB))^-sigma bCB;
In[63]:= FindRoot[{EqnA1,EqnB1,EqnC1},{pA,pA0},{pB,pB0},{pC,pC0}]
Out[63]= {pA->0.9977,pB->1.00969,pC->0.9977}
In[64]:= pA1=pA/.%;
In[65]:= pB1=pB/.%%;
In[66]:= pC1=pC/.%%%;
In[67]:= PA1=(pA1^(1-sigma)+bBA (pB1 (1+tBA))^(1-sigma)+bCA (pC1 (1+tCA))^(1-sigma))^(1/(1-sigma));
In[68]:= PB1=(pB1^(1-sigma)+bAB (pA1 (1+tAB))^(1-sigma)+bCB (pC1(1+tCB))^(1-sigma))^(1/(1-sigma));
In[69]:= PC1=(pC1^(1-sigma)+bBC (pB1 (1+tBC))^(1-sigma)+bAC (pA1 (1+tAC))^(1-sigma))^(1/(1-sigma));
In[70]:= qAA1=kA PA1^(sigma+etaA) pA1^-sigma;
In[71]:= qAB1=kB PB1^(sigma+etaB) (pA1 (1+tAB))^-sigma bAB;
In[72]:= qAC1=kC PC1^(sigma+etaC) (pA1 (1+tAC))^-sigma bAC;
In[73]:= qBB1=kB PB1^(sigma+etaB) pB1^-sigma;
In[74]:= qBA1=kA PA1^(sigma+etaA) (pB1 (1+tBA))^-sigma bBA;
In[75]:= qBC1=kC PC1^(sigma+etaC) (pB1 (1+tBC))^-sigma bBC;
In[76]:= qCC1=kC PC1^(sigma+etaC) pC1^-sigma;
In[77]:= qCB1=kB PB1^(sigma+etaB) (pC1 (1+tCB))^-sigma bCB;
In[78]:= qCA1=kA PA1^(sigma+etaA) (pC1 (1+tCA))^-sigma bCA;
Percent Changes in Producer Prices
Supplier A
In[79]:= ((pA1-pA0) 100)/pA0
Out[79]= -0.230032
Supplier B
In[80]:= ((pB1-pB0) 100)/pB0
Out[80]= 0.968785
Supplier C
In[81]:= ((pC1-pC0) 100)/pC0
Out[81]= -0.230032
Percent Changes in Quantities
Domestic Shipments in A
In[82]:= ((qAA1-qAA0) 100)/qAA0
Out[82]= -5.48559
Exports of A to B
In[83]:= ((qAB1-qAB0) 100)/qAB0
Out[83]= 1.02548
Exports of A to C
In[84]:= ((qAC1-qAC0) 100)/qAC0
Out[84]= 1.02548
Domestic Shipments in B
In[85]:= ((qBB1-qBB0) 100)/qBB0
Out[85]= -2.53044
Exports of B to A
In[86]:= ((qBA1-qBA0) 100)/qBA0
Out[86]= 21.3708
Exports of B to C
In[87]:= ((qBC1-qBC0) 100)/qBC0
Out[87]= -2.53044
Domestic Shipments in C
In[88]:= ((qCC1-qCC0) 100)/qCC0
Out[88]= 1.02548
Exports of C to A
In[89]:= ((qCA1-qCA0) 100)/qCA0
Out[89]= -5.48559
Exports of C to B
In[90]:= ((qCB1-qCB0) 100)/qCB0
Out[90]= 1.02548
Percent Change in Consumer Expenditures on Imports and Domestic Shipments
Domestic Shipments in A
In[91]:= ((pA1 qAA1-pA0 qAA0) 100)/(pA0 qAA0)
Out[91]= -5.70301
Exports of A to B
In[92]:= ((pA1 (1+tAB) qAB1-pA0 (1+tAB0) qAB0) 100)/(pA0 (1+tAB0) qAB0)
Out[92]= 0.793084
Exports of A to C
In[93]:= ((pA1 (1+tAC) qAC1-pA0 (1+tAC0) qAC0) 100)/(pA0 (1+tAC0) qAC0)
Out[93]= 0.793084
Domestic Shipments in B
In[94]:= ((pB1 qBB1-pB0 qBB0) 100)/(pB0 qBB0)
Out[94]= -1.58617
Exports of B to A
In[95]:= ((pB1 (1+tBA) qBA1-pB0 (1+tBA0) qBA0) 100)/(pB0 (1+tBA0) qBA0)
Out[95]= 11.406
Exports of B to C
In[96]:= ((pB1 (1+tBC) qBC1-pB0 (1+tBC0) qBC0) 100)/(pB0 (1+tBC0) qBC0)
Out[96]= -1.58617
Domestic Shipments in C
In[97]:= ((pC1 qCC1-pC0 qCC0) 100)/(pC0 qCC0)
Out[97]= 0.793084
Exports of C to A
In[98]:= ((pC1 (1+tCA) qCA1-pC0 (1+tCA0) qCA0) 100)/(pC0 (1+tCA0) qCA0)
Out[98]= -5.70301
Exports of C to B
In[99]:= ((pC1 (1+tCB) qCB1-pC0 (1+tCB0) qCB0) 100)/(pC0 (1+tCB0) qCB0)
Out[99]= 0.793084